According to their research, the Hungarian Cardinal Peter Erdö led the field of favourites in the first round of voting.
He was followed by Robert Francis Prevost, who was later elected Pope, and Cardinal Pietro Parolin.
The book was published in Spain on Wednesday.
The authors also look in detail at the question of why the first round of voting began with a significant delay.
Black smoke only appeared at 9 pm that day instead of around 7 pm as expected. It was already known that Cardinal Raniero Cantalamessa had extended his introductory words - by around an hour.
Piqué and O'Connell now cite another reason: a mobile phone in the Sistine Chapel.
An elderly cardinal had forgotten to hand in his mobile phone; only after this omission had been rectified was the voting able to begin.
Strict rules apply in the Vatican during the papal election.
The cardinals entitled to vote are completely sealed off, have to hand in their mobile phones and the mobile phone network is deactivated.
According to research, this led to some cardinals oversleeping at the beginning of the conclave - without a mobile phone, they had no alarm clock.
Vatican employees reportedly had to wake them up; later, the Vatican distributed special alarm clocks to the cardinals.
On around 450 pages, Piqué and O'Connell present numerous background information and anecdotes about the conclave in diary-like form.